解析学火曜セミナー

開催情報 火曜日　16:50～18:20　数理科学研究科棟(駒場) 128号室 石毛 和弘, 坂井 秀隆, 伊藤 健一 https://www.ms.u-tokyo.ac.jp/seminar/analysis/

2019年03月05日(火)

16:50-18:20   数理科学研究科棟(駒場) 128号室
Nicholas Edelen 氏 (Massachusetts Institute of Technology)
The structure of minimal surfaces near polyhedral cones (English)
[ 講演概要 ]
We prove a regularity theorem for minimal varifolds which resemble a cone $C_0$ over an equiangular geodesic net. For varifold classes admitting a no-hole'' condition on the singular set, we additionally establish regularity near the cone $C_0 \times R^m$. Our result implies the following generalization of Taylor's structure theorem for soap bubbles: given an $n$-dimensional soap bubble $M$ in $R^{n+1}$, then away from an $(n-3)$-dimensional set, $M$ is locally $C^{1,\alpha}$ equivalent to $R^n$, a union of three half-$n$-planes meeting at $120$ degrees, or an $(n-2)$-line of tetrahedral junctions. This is joint work with Maria Colombo and Luca Spolaor.